Optical vibrational modes of Ge nanowires: A

Microelectronic Engineering 159 (2016) 215–220

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Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee

Optical vibrational modes of Ge nanowires: A computational approach A. Trejo, A. Miranda, L.K. Toscano-Medina, R. Vázquez-Medina, M. Cruz-Irisson ⁎ ESIME Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana 1000, 04430 Cd. de México, México

a r t i c l e

i n f o

Article history: Received 18 December 2015 Received in revised form 19 April 2016 Accepted 23 April 2016 Available online 27 April 2016 Keywords: Germanium nanowires Density functional perturbation theory Phonons Raman spectrum

a b s t r a c t Although Ge nanowires (GeNWs) have been extensively studied in the last decade the information about their vibrational modes is still scarce, their correct comprehension could hasten the development of new microelectronic technologies, therefore, in this work we aimed to study the vibrational properties, Raman and IR and spectrum of GeNWs using the first principles density functional perturbation theory. The nanowires are modelled in the [001] direction and all dangling bonds are passivated with H and Cl atoms. Results show that the vibrational modes can be classified in three frequency intervals, a low frequency one (between 0 and 300 cm−1) of mainly Ge\\Ge vibrations, and two of Ge\\H bending and stretching vibrations (400–500 cm−1 and 2000 cm−1, respectively). There is a shift of the highest optical modes of Ge\\Ge vibrations compared to their bulk counterparts due to phonon confinement effects, however it is masked by some Ge\\H bond bending modes as demonstrated by the IR and Raman responses. The Cl passivated case shows a larger number of modes at lower frequencies due to the higher mass of Cl compared to H, which in turn reduces the red shift of the highest optical modes frequencies. These results could be important for the characterization of GeNWs with different surface passivations. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Currently technology is incorporated in almost every facet of human life, as the development of new electronic devices for communications, amusement, and work demands more efficient microelectronic components such as transistors, sensors, diodes switches among others. While the capacity of miniaturization of the technology increases, some fundamental physical limits of device fabrications are about to be reached, thus requiring the progress of new materials which would allow a better performance in lower sizes, the nanostructured materials are ideal candidates to this end specially the semiconductor nanowires. In recent years these low dimensional systems have gathered significant attention due to their potential applications, especially Germanium nanowires (GeNWs) could be used in microelectronics devices such as in infrared detectors [1], Schottky solar cells [2], solar cells [3], sensors [4] and lithium-ion batteries [5]. There are numerous experimental investigations of GeNWs, however there have been seldom theoretical investigations, mainly focused on the electronic properties such as the work of Arantes and Fazzio [6] which studies the electronic properties of [110, 111] oriented nanowires, or the work of Jing and coworkers [7] who analyze the effects of surface passivation with ethyl groups and anisotropy on the electronic properties of GeNWs, or the more recent studies that study the effects of halogens on the surface passivation [8], core-shell structures [9–11], and water induced electrical hysteresis [12]. The vibrational properties of GeNWs are much less studied, where are only a handful of works ⁎ Corresponding author. E-mail address: [email protected] (M. Cruz-Irisson).

http://dx.doi.org/10.1016/j.mee.2016.04.024 0167-9317/© 2016 Elsevier B.V. All rights reserved.

like the one of Peelaers [13] and collaborators which investigate the effects of doping on the vibrational properties, or previous works [14,15] which use semi-empirical potentials to study the Raman response and vibrational properties of GeNWs identifying the effects of the phonon confinement such as a red shift of the highest optical modes and an asymmetrical broadening of the Raman peaks, and there are none, (at the best of our knowledge) that uses first principles methods to model the Raman an IR response of these nanostructures, which would prove to be helpful in the development of new technologies of GeNWs since both spectroscopies provide non-destructive tools for the characterization of these materials and provide insight on the effect of the confinement on their vibrational properties. Motivated by recent experimental results, in this work a study of the vibrational properties of GeNWs is developed using the first principles density functional perturbation theory, using the generalized gradient approximation and norm conserving pseudopotentials. The results show that the vibrational properties of these structures are heavily influenced by the surface configuration and confinement of the nanowires since a redshift and additional vibrational modes are generated around the highest optical mode frequency of bulk Ge. 2. Model and calculation scheme The nanowires were modelled using the supercell technique [16,17] by removing atoms outside of a circumference on the [001] direction of an otherwise perfect Ge crystal, at this time this direction was chosen since the [110] direction has already been studied by other group [13], and the other most common growth direction of Ge nanowires the [111] is too computationally expensive whereas the [001] has a

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reasonable computational cost, and although scarcely reported it has been experimentally synthetized [18]. Contrary to previous works using semi empirical potentials [14,15] where the surface was left unpassivated the nanowire surface dangling bonds were passivated with H atoms which have been observed experimentally [19], also to avoid negative frequencies product of the highly reactive surfaces as will be seen in the results section, also a nanowire was passivated with Cl in order to observe the effects of surface terminations on the vibrational properties of the nanowires, however due to computational constraints only one diameter was studied with this surface passivation as depicted in Fig. 1c). To quantify the effects of the quantum confinement on the vibrational properties, three nanowire diameters were modelled: 1.1, 0.9 and 0.6 nm as observed in Fig. 1(a–d). Although the diameters seem too small compared with experimental results [20] recently ultrathin nanowires have been observed [21]. Additionally due to periodic boundary conditions the supercell was chosen so a space of at least 12 Å was left between the nanowires and their replicas.

All vibrational properties IR and Raman spectrum calculations were performed using the first principles density functional perturbation theory as implemented in the CASTEP code [22,23], with a Perdew Burke Ernzerhof functional [24] within the generalized gradient approximation and norm conserving pseudopotentials [25]. The converged cutoff was of 720 eV for an error of 0.01 eV in the energy calculation of crystalline Ge, and the Monkhorst-Pack [26] grid was of 1 × 1 × 7 for the Brillouin zone sampling. The structures were optimized using the BFGS algorithm [27] where the convergence was achieved when the interatomic forces were less than 0.001 eV/Å, whereas the vibrational properties were converged to an error of 0.1 cm−1 with a difference of + 0.6 cm− 1 of the highest optical mode of germanium compared to the experimental value of 300.7 cm−1. The calculation parameters were tested on bulk crystalline Ge, the results can be observed in Fig. 2, where the theoretical calculations are compared with experimental results taken from [28,29]. It can be seen that there is an excellent agreement between the theoretical description

Fig. 1. Top and side view of GeNWs orientated on the [001] direction with diameters of: a) 1.1, b) 0.9 c) 0.9 Cl-passivated and d) 0.6 nm.


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Fig. 2. Phonon band structure and density of states of bulk crystalline Ge. The red spheres represent the experimental results taken from [28,29].

and the experimental results, thus validating the convergence test performed in the bulk semiconductor. 3. Results and discussion The phonon band structure of a 0.9 nm nanowire was calculated with and without passivation (bare) to observe the effects of the surface on the vibrational properties of the nanowires contrasted to some of the already known effects of phonon confinement [30], which have been studied on previous works in comparison with pGe and its effect on the specific heat of the GeNWs [16,17] however the Raman and IR responses and differences that arise due to a different surface terminations were not addressed. The main effects of phonon confinement area red shift of the highest optical mode frequencies compared to their bulk counterparts and an asymmetrical broadening of the Raman spectrum. In Fig. 3 the phonon band structure of the nonpassivated nanowire is contrasted with the H and Cl passivated ones, the passivated nanowires develop extra phonon bands due to the Ge\\H or Ge\\Cl bond vibrations, respectively which could be stretching and bending

modes. Further inspection of the phonon eigenvector corroborates that three intervals of frequency can be identified: the first from 0 to 300 cm−1 which accounts for Ge\\Ge bond vibrations independently of the surface passivation, the second one from 350 to 820 cm− 1 where the vibrational modes belong to Ge\\H (hydride) and Ge\\H2 (dihydride) bonds bending vibrations, and in the case of the Cl passivation Ge\\Cl and Ge\\Cl2 bonds stretching modes due to the higher mas of Cl compared to H, and finally the 1980 to 2000 cm−1 interval owning to hydride and dihydride bonds stretching modes. In contrast the bare nanowire exhibits only bands up to 262.33 cm− 1 which would be in accordance to the phonon confinement scheme, however there are negative (imaginary) frequency bands on its phonon band structure which indicates structural instabilities of the system [13] or a saddle point in the optimization of the energy surface [31]. Subsequent trials perturbing the system and optimizing the nanowire various times proved ineffective to remove such bands, hence concluding that this particular morphology cannot undergo surface reconstructions to achieve higher stability, hence the negative modes are inherent to the system indicating that this particular bare nanowire is unstable, mainly

Fig. 3. Phonon band structure of a) bare, b) H and c) Cl passivated GeNW of 0.9 nm of diameter.

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due to the dangling bonds on the surface which create a highly reactive surface. Finally on the Cl passivated case, a larger number of modes is observed around 0 to 150 cm− 1 compared to the other two cases, which is caused by the larger mas of Cl compared to H which shifts the bending and stretching modes to lower frequencies, while also diminishing the phonon confinement effects where the highest optical mode with a major Ge contribution has a frequency of 282 cm−1 which represents a lower shift than the bare and H passivated cases, due to the larger radius of Cl compared to H. It is worth noticing that the results are consistent in the three studied diameters (not pictured) where the bare nanowires exhibit negative frequencies in their phonon band structure and the H passivated ones show the three already mentioned frequency intervals, the clear separation between such intervals is attributed to the much higher mass of Ge compared to the H. Other feature worth mentioning is the lower redshift of the highest optical modes of the H and Cl passivated nanowires compared to the bare one (275 and 282 to 262 cm−1, respectively), this being consistent with previous works using semiempirical potentials [14], which could occur for the bending states of the surface hydrides around the highest optical modes, and in the Cl case its large atomic radius which accounts for a higher effective diameter of the nanowire. To inquire the origin of the lower shift a study of the partial phonon DOS of H and IR spectrum of the 0.9 nm nanowire is shown in Fig. 4. It can be seen in both that in fact, around 300 cm − 1 there is a small contribution of the H and Cl to the phonon DOS and a IR peak which indicates that there is a shift of the dipolar moment of the H\\Cl bonds on the surface of the nanowire, hence the effects of phonon confinement are, on a little scale, masked by states created by the surface dihydrides vibrations. These results could be useful in the characterization of the GeNWs since them indicate that the H and Cl bonds activity begins at low frequencies. Additionally it is worth noticing that although the majority of the peaks on the phonon DOS correspond to a peak in the IR spectrum, there are some particular frequencies where the IR is absent and the phonon DOS shows a slight activity specially on the H passivated case. Inspecting the eigenvectors on such frequencies the dipolar moment of the vibrations are nullified all through the surface of the nanowire, hence the absence of the IR peak. For these cases the Raman spectrum or the phonon DOS would achieve better results in identifying such

modes. Finally on Fig. 4 the mode with the highest IR intensity of the Cl passivated GeNW is illustrated on the right panel indicated with the ζ letter, this mode is particularly interesting since the phonon DOS indicates a mayor contribution of the Ge atoms compared to the Cl atoms which would be counterintuitive since there would be no shift of the overall dipolar moment, however upon analyzing the eigenvector and the vector diagram of this mode it can be seen that the high activity is due to two factors, a high displacement of the surface Ge atoms and a slight displacement of all surface Cl atoms which amounts to the high IR intensity. Finally, the highest optical mode Raman peak around 300 cm−1 was calculated in order to be compared to the experimental crystalline Ge one, the results are shown on Fig. 5. To better compare the Raman peaks with the experimental results, a Lorentzian fit with FWHM of 5 cm−1 was made to the highest frequency peak in order to clear the peaks that arise at lower frequencies and the broadening product of the smearing used to calculate the Raman spectrum. To compare the effects of surface termination, only the 0.8 nm– GeNW with the H and Cl passivation are pictured, while in the right panel (Fig. 5c)) the evolution with phonon quantum confinement of the highest Raman peak frequency is shown by obtaining the ratio between the calculated value (ωR) and the reference of crystalline Ge (ω0 = 300.7 cm−1). It can be seen clearly that there is a pronounced redshift especially for the 0.6 nm (270 cm−1 compared to 300.7 cm− 1 of crystalline bulk Ge) even with the masking caused by the surface H which corroborates the effect of the phonon confinement in this kind of structures. As the nanowire diameter increases, the Raman spectrum approaches to that of the crystalline Ge as expected, however due to the ultrathin nature of the nanowires here studied there is still a great gap between the crystalline Ge and the GeNWs value compared to the experimental results presented in [20]. Also it can be observed that while the frequency of the Raman peak is shifted towards a lower frequency compared to the crystalline Ge, the shift is lesser than the one with H passivation probably due to the higher mass and volume of the Cl atom, these results are especially interesting to the experimental characterization of these nanostructures. Results indicate that the phonon confinement effects are notable and the tendency can be seen even in models of ultrathin GeNWs with H and Cl surface passivation which could be of great importance to the development of microelectronic and thermoelectric devices.

Fig. 4. Ge, H, and Cl (green, gray and blue lines) compared to IR spectrum (red line) of a 0.8 nm nanowire with a) H and b) Cl surface passivations. In the inset the representation of the modes with frequencies that appear on the phonon DOS and not on the IR spectrum are depicted. On ζ the mode with the highest IR intensity is depicted with atom and vector representations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


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Fig. 5. Raman spectrum of a) crystalline Ge, and b) 0.8 nm GeNW with H (green line) and Cl (passivation). c) Evolution of the highest Raman peak (ωR/ω0 being the ratio between the highest Raman peak of the GeNW and the reference of 300.7 cm−1 of crystalline Ge) with respect to the diameter. The red spheres represent experimental data taken from [20]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4. Conclusions In summary the vibrational properties of Germanium nanowires were studied using the first principles density functional perturbation theory. The results show that there is a shift to lower frequencies of the highest optical modes compared to the bulk germanium mainly due to phonon confinement effects, however this shift is slightly masked by some surface effects as seen on IR and partial phonon DOS analysis. The H passivated GeNWs exhibit three clear intervals of main contributions of the bonds to the vibrational modes, for instance the first interval is mainly contributed by Ge\\Ge modes while the second and third intervals have main contributions from the hydride and dihydride bonds bending and stretching vibrations, respectively, while the Cl passivated ones have only two frequency intervals which combine Cl and Ge modes around 0 to 300 cm−1, and stretching modes around 500 cm− 1. The pronounced shift of the highest Raman peak around the bulk crystalline Ge frequency could be caused by the phonon confinement effects, which are more pronounced than in experimental literature due to the low diameter of the nanowires studied. These results could be important in the characterization of the GeNWs for future microelectronics applications. Acknowledgments This work was partially supported by CONACYT infrastructure project 20161770 and 20161771 and multidisciplinary project 20141640 by SIP, IPN, A.M. would like to thank for the financial support from CONACyT-Retención.. References [1] A. Solanki, K.B. Crozier, Germanium nanowires as spectrally-selective photodetectors in the visible-to-infrared, CLEO: 2015, Optical Society of America, San Jose, California 2015, p. SM1G.1. [2] J.-H. Yun, Y. Park, J. Kim, H.-J. Lee, W. Anderson, J. Park, Solution-processed germanium nanowire-positioned Schottky solar cells, Nanoscale Res. Lett. 6 (2011) 1–5. [3] E.C. Garnett, M.L. Brongersma, Y. Cui, M.D. McGehee, Nanowire solar cells, Annu. Rev. Mater. Res. 41 (2011) 269–295. [4] Y. Georgiev, R. Yu, N. Petkov, O. Lotty, A. Nightingale, J. deMello, R. Duffy, J. Holmes, Silicon and germanium junctionless nanowire transistors for sensing and digital electronics applications, in: A. Nazarov, F. Balestra, V. Kilchytska, D. Flandre (Eds.), Functional Nanomaterials and Devices for Electronics, Sensors and Energy Harvesting, Springer International Publishing 2014, pp. 367–388.

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